请帮我写一个高阶矩阵求逆MPI并行化程序，用c语言，使用高斯-约旦消元法来求解逆矩阵

好的，以下是使用高斯-约旦消元法来求解逆矩阵的MPI并行化程序示例：

#include <stdio.h>
#include <stdlib.h>
#include <mpi.h>

void print_matrix(double* matrix, int rows, int cols) {
    for (int i = 0; i < rows; i++) {
        for (int j = 0; j < cols; j++) {
            printf("%f ", matrix[i * cols + j]);
        }
        printf("\n");
    }
}

void matrix_inverse(double* matrix, int N) {
    // 构造增广矩阵
    double* augment = malloc(N * 2 * sizeof(double));
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            augment[i * (N * 2) + j] = matrix[i * N + j];
        }
        for (int j = N; j < N * 2; j++) {
            augment[i * (N * 2) + j] = (i == j - N) ? 1 : 0;
        }
    }

    // 高斯-约旦消元
    for (int i = 0; i < N; i++) {
        double pivot = augment[i * (N * 2) + i];
        for (int j = 0; j < N * 2; j++) {
            augment[i * (N * 2) + j] /= pivot;
        }
        for (int j = 0; j < N; j++) {
            if (j == i) continue;
            double factor = augment[j * (N * 2) + i];
            for (int k = 0; k < N * 2; k++) {
                augment[j * (N * 2) + k] -= factor * augment[i * (N * 2) + k];
            }
        }
    }

    // 提取逆矩阵
    for (int i = 0; i < N; i++) {
        for (int j = N; j < N * 2; j++) {
            matrix[i * N + j - N] = augment[i * (N * 2) + j];
        }
    }

    free(augment);
}

int main(int argc, char** argv) {
    MPI_Init(&argc, &argv);

    int rank, size;
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &size);

    // 生成矩阵
    int N = 4;
    double* matrix = NULL;
    if (rank == 0) {
        matrix = malloc(N * N * sizeof(double));
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                matrix[i * N + j] = rand() % 10;
            }
        }
        printf("原矩阵：\n");
        print_matrix(matrix, N, N);
    }

    // 矩阵分割
    int local_rows = N / size; // 每个进程处理的行数
    double* local_matrix = malloc(local_rows * N * sizeof(double));
    MPI_Scatter(matrix, local_rows * N, MPI_DOUBLE,
                local_matrix, local_rows * N, MPI_DOUBLE, 0, MPI_COMM_WORLD);

    // 对小矩阵求逆
    for (int i = 0; i < local_rows; i++) {
        matrix_inverse(&local_matrix[i * N], N);
    }

    // 将所有小矩阵合并到主进程中
    double* inv_matrix = NULL;
    if (rank == 0) {
        inv_matrix = malloc(N * N * sizeof(double));
    }
    MPI_Gather(local_matrix, local_rows * N, MPI_DOUBLE,
               inv_matrix, local_rows * N, MPI_DOUBLE, 0, MPI_COMM_WORLD);

    // 输出逆矩阵
    if (rank == 0) {
        printf("逆矩阵：\n");
        print_matrix(inv_matrix, N, N);
    }

    MPI_Finalize();
    return 0;
}

这个程序首先生成一个随机矩阵，并将其分割成多个小矩阵。然后，每个进程都对自己分配到的小矩阵进行求逆操作，并使用`MPI_Gather`函数将所有小矩阵合并到主进程中。最后，主进程输出逆矩阵。